Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrodinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.

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Two-dimensional gas of massless Dirac fermions in graphene

Although gold is the subject of one of the most ancient themes of investigation in science, its renaissance now leads to an exponentially increasing number of publications, especially in the context of emerging nanoscience and nanotechnology with nanoparticles and self-assembled monolayers (SAMs). We will limit the present review to gold nanoparticles (AuNPs), also called gold colloids. AuNPs are the most stable metal nanoparticles, and they present fascinating aspects such as their assembly of multiple types involving materials science, the behavior of the individual particles, size-related electronic, magnetic and optical properties (quantum size effect), and their applications to catalysis and biology. Their promises are in these fields as well as in the bottom-up approach of nanotechnology, and they will be key materials and building block in the 21st century. Whereas the extraction of gold started in the 5th millennium B.C. near Varna (Bulgaria) and reached 10 tons per year in Egypt around 1200-1300 B.C. when the marvelous statue of Touthankamon was constructed, it is probable that “soluble” gold appeared around the 5th or 4th century B.C. in Egypt and China. In antiquity, materials were used in an ecological sense for both aesthetic and curative purposes. Colloidal gold was used to make ruby glass 293 Chem. Rev. 2004, 104, 293−346

Gold nanoparticles: assembly, supramolecular chemistry, quantum-size-related properties, and applications toward biology, catalysis, and nanotechnology.

We demonstrate how by taking better account of electron correlations in the $3d$ shell of metal ions in nickel oxide it is possible to improve the description of both electron energy loss spectra and parameters characterizing the structural stability of the material compared with local spin density functional theory.

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Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study

Spintronics, or spin electronics, involves the study of active control and manipulation of spin degrees of freedom in solid-state systems. This article reviews the current status of this subject, including both recent advances and well-established results. The primary focus is on the basic physical principles underlying the generation of carrier spin polarization, spin dynamics, and spin-polarized transport in semiconductors and metals. Spin transport differs from charge transport in that spin is a nonconserved quantity in solids due to spin-orbit and hyperfine coupling. The authors discuss in detail spin decoherence mechanisms in metals and semiconductors. Various theories of spin injection and spin-polarized transport are applied to hybrid structures relevant to spin-based devices and fundamental studies of materials properties. Experimental work is reviewed with the emphasis on projected applications, in which external electric and magnetic fields and illumination by light will be used to control spin and charge dynamics to create new functionalities not feasible or ineffective with conventional electronics.

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Spintronics: Fundamentals and applications

In Weiterentwicklung fruherer Theorien von J. und F. Perrin und klassischphysikalischer Uberlegungen des Verfassers wird eine quantenmechanische Behandlung des Ubergangs von Elektronenanregungsenergie zwischen gleichartigen Molekulen in Losung gegeben. Der kritische Molekulabstand, unterhalb dessen der ubergang wahrend der Anregungsdauer stattfindet, last sich aus den Absorptions- und Fluoreszenzspektren und der Anregungsdauer der Molekule berechnen. Fur Fluorescein und Chlorophyll a ergeben sich Werte von 50 bzw. 80 AE, entsprechend den mittleren Molekulabstanden in Losungen von 3,2 · 10−3 bzw. 7,7 · 10−4 Molen/Liter. Fur die Bereiche oberhalb und unterhalb der kritischen Konzentration werden Formeln zur Berechnung der Energieabwanderung vom Primarmolekul angegeben, die mit den vorliegenden Messungen der Konzentrationsdepolarisation der Fluoreszenz gut ubereinstimmen. Die Anwendung auf analoge Energiewanderungsprobleme in Molekulkristallen und im Assimilationsapparat der Pflanze wird diskutiert.

Zwischenmolekulare Energiewanderung und Fluoreszenz

1. Introduction 2. Theory of Electrons in a Non-Crystalline Medium 3. Phonons and Polarons 4. The Fermi Glass and the Anderson Transition 5. Liquid Metals and Semimetals 6. Non-Crystalline Semiconductors 7. Tetrahedrally-Bonded Semiconductors - Amorphous Germanium and Silicon 8. Aresnic and Other Three-Fold Co-ordinated Materials 9. Chalcogenide and Other Glasses 10. Selenium, Tellurium, and their Alloys

Electronic processes in non-crystalline materials

The experimental evidence concerning the density of states in amorphous semiconductors and the ranges of energy in which states are localized is reviewed; this includes d.c. and a.c. conductivity, drift mobility and optical absorption. There is evidence that for some chalcogenide semiconductors the model proposed by Cohen, Fritzsche and Ovshinsky (1969) should be modified by introducing a band of localized states, near the centre of the gap. The values of C, when the d.c. conductivity is expressed as C exp (- E/kT), are considered. The behaviour of the optical absorption coefficient near the absorption edge and its relation to exciton formation are discussed. Finally, an interpretation of some results on photoconductivity is offered.

Conduction in non-crystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors

Volume II of this work covers many-body problems and applications of the theory to electron collisions with atoms, collisions between atomic systems, nuclear collisions, certain aspects of two-body systems under relativistic collisions, and the use of time-dependent perturbation theory. Despite the amount of work carried out since this book was first published, the underlying theory presented here remains both sound and of practical value to all theoretical physicists.

The theory of atomic collisions

In a discussion of conduction in glasses containing transition metal ions, the following points are stressed: 1. (a) The process is similar to “impurity conduction” in doped and compensated semi-conductors. 2. (b) There should be two terms in the activation energy, the Miller-Abrahams term and a polaron hopping term. 3. (c) Both terms should tend to zero, giving a decreasing slope of the ln p versus 1/T curve, as T → 0. 4. (d) The Heikes-Ure formula for the thermopower is discussed and a tentative explanation given of the difference between vanadium- and iron-containing glasses.

Conduction in glasses containing transition metal ions

A discussion is given of some aspects of the metal insulator transition. Particular attention is paid to the status of the “minimum metallic conductivity”. The concept is valid for liquids, and in some, but not all, solid systems.

Nevill Mott

Papers

Electronic processes in non-crystalline materials

Conduction in non-crystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors

The theory of atomic collisions

Conduction in glasses containing transition metal ions

Metal-insulator transitions